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Valuations

Valuations correspond to orbits of points on a curve: every orbit of Frobenius gives a valuation, and every valuation gives an orbit. This will be elaborated in Chapter 5. In this chapter, we study how valuations distinguish constants from nonconstant functions and how valuations can ramify.

We first develop this theory for an arbitrary extension L/K. In Section 1.4, we apply our theory to the situation that is the subject of this book, where L/K is a finite extension K/q of the field of rational functions over the finite field of constants

The embedding corresponds to the projection where a point on the curve projects to the ...

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